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Algorithms for Sparsity-Constrained Optimization

Part of the Springer Theses Book Series (volume 261)

DOI: 10.1007/978-3-319-01881-2

ISBN: 978-3-319-01880-5

Publisher: Springer International Publishing - Springer Journals

Sep 3, 2013

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Chapter 1Introduction

Bahmani, Sohail

Pages: 1 –3

[Applications that require analysis of high-dimensional data have grown significantly during the past decade. In many of these applications, such as bioinformatics, social networking, and mathematical finance, the dimensionality of the data is usually much larger than the number of samples or...
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Chapter 2Preliminaries

Bahmani, Sohail

Pages: 5 –10

[Least squares problems occur in various signal processing and statistical inference applications.]
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Chapter 3Sparsity-Constrained Optimization

Bahmani, Sohail

Pages: 11 –35

[Theoretical and application aspects of sparse estimation in linear models have been studied extensively in areas such as signal processing, machine learning, and statistics. The sparse linear regression and CS algorithms attempt to provide a sparse vector whose consistency with the acquired data...
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Chapter 41-Bit Compressed Sensing

Bahmani, Sohail

Pages: 37 –49

[Quantization is an indispensable part of digital signal processing and digital communications systems. To incorporate CS methods in these systems, it is thus necessary to analyze and evaluate them considering the effect of measurement quantization.]
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Chapter 5Estimation Under Model-Based Sparsity

Bahmani, Sohail

Pages: 51 –60

[Beyond the ordinary, extensively studied, plain sparsity model, a variety of structured sparsity models have been proposed in the literature Bach (2008); Roth and Fischer (2008); Jacob et al. (2009); Baraniuk et al. (2010); Bach (2010); Bach et al. (2012); Chandrasekaran et al. (2012);...
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Chapter 6Projected Gradient Descent for ℓp-Constrained Least Squares

Bahmani, Sohail

Pages: 61 –69

[As mentioned in Chap. 2, to avoid the combinatorial computational cost of (2.2), often the ℓ0-norm is substituted by the ℓ1-norm to reach at a convex program.]
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Chapter 7Conclusion and Future Work

Bahmani, Sohail

Pages: 71 –72

[In this thesis, we studied sparsity-constrained optimization problems and proposed a number of greedy algorithms as approximate solvers for these problems. Unlike the existing convex programming methods, the proposed greedy methods do not require the objective to be convex everywhere and produce...

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